The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes bothcontemporary and dynamic linear relationships between component processes of the multivariate system.In this article we develop novel inference procedures for the spectral density matrix in the high-dimensionalsetting. Specifically, we introduce a new global testing procedure to test the nullity of the cross-spectraldensity for a given set of frequencies and across pairs of component indices. For the first time, both Gaussianapproximation and parametric bootstrap methodologies are employed to conduct inference for a high-dimensional parameter formulated in the frequency domain, and new technical tools are developed toprovide asymptotic guarantees of the size accuracy and power for global testing. We further propose amultiple testing procedure for simultaneously testing the nullity of the cross-spectral density at a givenset of frequencies. The method is shown to control the false discovery rate. Both numerical simulationsand a real data illustration demonstrate the usefulness of the proposed testing methods. Supplementarymaterials for this article are available online, including a standardized description of the materials availablefor reproducing the work.
Publication:
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION2025, VOL. 00, NO. 0, 1–15: Theory and Methods
https://doi.org/10.1080/01621459.2025.2468013
Author:
Jinyuan Chang
Laboratory of Data Science and Business Intelligence, Southwestern University of Finance and Economics, Chengdu, Sichuan, China
Big Data Laboratory on Financial Security and Behavior (MOE Philosophy and Social Sciences Laboratory), Southwestern University of Finance and Economics, Chengdu, Sichuan, China
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Qing Jiang
Faculty of Arts and Sciences,Beijing Normal University, Zhuhai, China
Tucker McElroy
Research and Methodology Directorate, U.S. Census Bureau, Washington, DC
Xiaofeng Shao
Department of Statistics and Data Science, and Department of Economics, Washington University in St Louis, St. Louis, MO
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